Fluid–structure interaction analysis of the two-dimensional flag-in-wind problem by an interface-tracking ALE finite element method

Zhang and co-workers [Zhang J, Childress S, Libchaber A, Shelley M. Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 2000;408:835–9] recently found that a flexible filament in a flowing soap film can exhibit three stable dynamical states; stretched-straight, flapping, and bistable states. When this experimental model is regarded as an one-dimensional flag in a two-dimensional fluid flow, their findings contradict the common idea that flags always flap in a wind. In this paper, the filament-in-soap film problem is simulated by a fluid–structure interaction finite element method as a two-dimensional version of a flag-in-wind problem, where Navier–Stokes equations based on the arbitrary Lagrangian–Eulerian (ALE) method are strongly coupled with the Lagrangian equilibrium equations of the structure. In our simulations, the three states are successfully reproduced, and the effects of some representative parameters on the amplitude and frequency of oscillations are investigated to reveal the underlying mechanism of flag flapping.